{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA——对半导体制造数据降维\n",
    "\n",
    "降维的目标就是对输入的数目进行削减，由此剔除数据中的噪声并提高机器学习方法的性能。\n",
    "\n",
    "PCA优点：降低数据的复杂性，识别最重要的多个特征。\n",
    "\n",
    "缺点：不一定需要，可能损失有用的信息。\n",
    "\n",
    "适用数据类型：数值型数据"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**NumPy实现PCA伪代码：**\n",
    "```\n",
    "\n",
    "去除平均值\n",
    "\n",
    "计算协方差矩阵\n",
    "\n",
    "计算协方差矩阵的特征向量和特征值\n",
    "\n",
    "将特征值从大到小排序\n",
    "\n",
    "保留最上面的N个特征向量\n",
    "\n",
    "将数据转换到上述N个特征向量构建的新空间中\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import *\n",
    "\n",
    "def loadDataSet(fileName, delim='\\t'):\n",
    "    with open(fileName) as f:\n",
    "        stringArr = [line.strip().split(delim) for line in f.readlines()]\n",
    "        datArr = [list(map(float, line)) for line in stringArr]\n",
    "        return mat(datArr)\n",
    "    \n",
    "def pca(dataMat, topNfeat=9999999):\n",
    "    #1.去平均值\n",
    "    meanVals = mean(dataMat, axis=0)\n",
    "    meanRemoved = dataMat - meanVals\n",
    "    covMat = cov(meanRemoved, rowvar=0)\n",
    "    eigVals, eigVects = linalg.eig(mat(covMat))\n",
    "    #2.从大到小对N个值进行排序\n",
    "    eigValInd = argsort(eigVals)\n",
    "    eigValInd = eigValInd[:-(topNfeat+1):-1]\n",
    "    redEigVects = eigVects[:,eigValInd]\n",
    "    #3.将数据转换到新空间\n",
    "    lowDDataMat = meanRemoved * redEigVects\n",
    "    reconMat = (lowDDataMat * redEigVects.T) + meanVals #重构数据\n",
    "    return lowDDataMat, reconMat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataMat = loadDataSet('testSet.txt')\n",
    "lowDMat, reconMat = pca(dataMat, 1)\n",
    "# lowDMat, reconMat = pca(dataMat, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 1)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shape(lowDMat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2485388ab38>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.scatter(dataMat[:,0].flatten().A[0], dataMat[:,1].flatten().A[0], marker='^', s=90)\n",
    "ax.scatter(reconMat[:,0].flatten().A[0], reconMat[:,1].flatten().A[0], marker='o', s=10, c='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "#将NaN替换为平均值\n",
    "def replaceNanWithMean():\n",
    "    dataMat = loadDataSet('secom.data', ' ')\n",
    "    numFeat = shape(dataMat)[1] #计算特征数\n",
    "    for i in range(numFeat):\n",
    "        #1.计算所有特征的平均值\n",
    "        meanVal = mean(dataMat[nonzero(~isnan(dataMat[:,i].A))[0], i])\n",
    "        #2.将所有Nan置为平均值\n",
    "        dataMat[nonzero(isnan(dataMat[:,i].A))[0], i] = meanVal\n",
    "    return dataMat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataMat = replaceNanWithMean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "meanVals = mean(dataMat, axis=0)\n",
    "meanRemoved = dataMat - meanVals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "covMat = cov(meanRemoved, rowvar=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "eigVals, eigVects = linalg.eig(mat(covMat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.34151979e+07,  2.17466719e+07,  8.24837662e+06,  2.07388086e+06,\n",
       "        1.31540439e+06,  4.67693557e+05,  2.90863555e+05,  2.83668601e+05,\n",
       "        2.37155830e+05,  2.08513836e+05,  1.96098849e+05,  1.86856549e+05,\n",
       "        1.52422354e+05,  1.13215032e+05,  1.08493848e+05,  1.02849533e+05,\n",
       "        1.00166164e+05,  8.33473762e+04,  8.15850591e+04,  7.76560524e+04,\n",
       "        6.66060410e+04,  6.52620058e+04,  5.96776503e+04,  5.16269933e+04,\n",
       "        5.03324580e+04,  4.54661746e+04,  4.41914029e+04,  4.15532551e+04,\n",
       "        3.55294040e+04,  3.31436743e+04,  2.67385181e+04,  1.47123429e+04,\n",
       "        1.44089194e+04,  1.09321187e+04,  1.04841308e+04,  9.48876548e+03,\n",
       "        8.34665462e+03,  7.22765535e+03,  5.34196392e+03,  4.95614671e+03,\n",
       "        4.23060022e+03,  4.10673182e+03,  3.41199406e+03,  3.24193522e+03,\n",
       "        2.74523635e+03,  2.35027999e+03,  2.16835314e+03,  1.86414157e+03,\n",
       "        1.76741826e+03,  1.70492093e+03,  1.66199683e+03,  1.53948465e+03,\n",
       "        1.33096008e+03,  1.25591691e+03,  1.15509389e+03,  1.12410108e+03,\n",
       "        1.03213798e+03,  1.00972093e+03,  9.50542179e+02,  9.09791361e+02,\n",
       "        8.32001551e+02,  8.08898242e+02,  7.37343627e+02,  6.87596830e+02,\n",
       "        5.64452104e+02,  5.51812250e+02,  5.37209115e+02,  4.93029995e+02,\n",
       "        4.13720573e+02,  3.90222119e+02,  3.37288784e+02,  3.27558605e+02,\n",
       "        3.08869553e+02,  2.46285839e+02,  2.28893093e+02,  1.96447852e+02,\n",
       "        1.75559820e+02,  1.65795169e+02,  1.56428052e+02,  1.39671194e+02,\n",
       "        1.28662864e+02,  1.15624070e+02,  1.10318239e+02,  1.08663541e+02,\n",
       "        1.00695416e+02,  9.80687852e+01,  8.34968275e+01,  7.53025397e+01,\n",
       "        6.89260158e+01,  6.67786503e+01,  6.09412873e+01,  5.30974002e+01,\n",
       "        4.71797825e+01,  4.50701108e+01,  4.41349593e+01,  4.03313416e+01,\n",
       "        3.95741636e+01,  3.74000035e+01,  3.44211326e+01,  3.30031584e+01,\n",
       "        3.03317756e+01,  2.88994580e+01,  2.76478754e+01,  2.57708695e+01,\n",
       "        2.44506430e+01,  2.31640106e+01,  2.26956957e+01,  2.16925102e+01,\n",
       "        2.10114869e+01,  2.00984697e+01,  1.86489543e+01,  1.83733216e+01,\n",
       "        1.72517802e+01,  1.60481189e+01,  1.54406997e+01,  1.48356499e+01,\n",
       "        1.44273357e+01,  1.42318192e+01,  1.35592064e+01,  1.30696836e+01,\n",
       "        1.28193512e+01,  1.22093626e+01,  1.15228376e+01,  1.12141738e+01,\n",
       "        1.02585936e+01,  9.86906139e+00,  9.58794460e+00,  9.41686288e+00,\n",
       "        9.20276340e+00,  8.63791398e+00,  8.20622561e+00,  8.01020114e+00,\n",
       "        7.53391290e+00,  7.33168361e+00,  7.09960245e+00,  7.02149364e+00,\n",
       "        6.76557324e+00,  6.34504733e+00,  6.01919292e+00,  5.81680918e+00,\n",
       "        5.44653788e+00,  5.12338463e+00,  4.79593185e+00,  4.47851795e+00,\n",
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      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigVals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run extras/createFig1.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run extras/createFig2.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run extras/createFig3.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run extras/createFig4.py"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
